5-5 Solving Multi-Step Equations and Inequalities
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1 Solve. Graph the solution on a number line. 2(k 20 The solution is k (3r 34 The solution is r8. 2(g 1) > g 4 The solution is g < 2. esolutions Manual - Powered by Cognero Page 1
2 5p p + 6) The solution is p 6( 2z + 5) < 19z + 16 The solution is z < 2. 10p p 4) The solution is p esolutions Manual - Powered by Cognero Page 2
3 Solve. Check your solution. 12z + 4 = 2(5z + 8) 12 Check: d 12 = 4(d 6) Check: esolutions Manual - Powered by Cognero Page 3
4 3x + 2 = 2(2x 7) Check: 6(y 5) = 2(10 + 3y) The statement 30 = 20 is never true. The equation has no solutions and the solution set is. 4(2c + 8) = 5(c + 4) Check: esolutions Manual - Powered by Cognero Page 4
5 p = 3(3 + 4p ) The statement 10 = 9 is never true. The equation has no solutions and the solution set is. 3x (x 1) = 8x + 17 The statement 3 = 17 is never true. The equation has no solutions and the solution set is. 10z + 4 = 2(5z + 8) 12 The statement 4 = 4 is always true. The equation is an identity and the solution set is all numbers. GEOMETRY The perimeter of a rectangle is 50 centimeters. The length of the rectangle is one more than 3 times the width of the rectangle. What are the dimensions of the rectangle? The perimeter of a rectangle is 50 centimeters. Let w = the width of the rectangle. The length of the rectangle is one more than 3 times the width of the rectangle. So, the length l = 1 + 3w. Use the formula for perimeter, P = 2l + 2w. The width of the rectangle is 6 cm, and the length of the rectangle is 1 + 3(6), or 19 cm. esolutions Manual - Powered by Cognero Page 5
6 FINANCIAL LITERACY Tim is taking the train to Seattle to visit his grandparents. He was given $15 to spend on snacks and reading material. Granola bars cost $1.15 each, and magazines cost $1.25. If Tim buys the same number of granola bars and magazines, how many can he buy? Tim has at most $15 to spend on snacks and reading material. Let x = the number of granola bars he buys. Since Tim buys the same number of granola bars and magazines, then x = the number of magazines. Each granola bar costs $1.15, and each magazine cost $1.25. Tim can buy at most 6 granola bars and 6 magazines. Solve. Graph the solution on a number line. 20 > 5(w + 3) The solution is w < 1. h + 2) + 4 The solution is h2. esolutions Manual - Powered by Cognero Page 6
7 3(6m The solution is m 10(3 + s) < 4s The solution is s < 5. 3y 6 > 4(y 3) The solution is y < 6. esolutions Manual - Powered by Cognero Page 7
8 8(2h h + 20 The solution is h7. 3(3rr The solution is r9. 14t 28 < 7(t + 6) The solution is t< 10. esolutions Manual - Powered by Cognero Page 8
9 SCHOOL Nomar has earned scores of 73, 85, 91, and 82 on the first four of five math tests for the grading period. He would like to finish the grading period with a test average of at least 82. What is the minimum score Nomar needs to earn on the fifth test in order to achieve his goal? Nomar wants his average to be at least 82. He earned scores of 73, 85, 91, and 82 on the first four tests. Let s = his score on the fifth test. Nomar must score at least a 79 on the fifth test. Solve. 0.2(3c + 15) = 3(0.8c 8) Solve each inequality. Graph the solution on a number line. 25t The solution is t with an arrow to the right. esolutions Manual - Powered by Cognero Page 9
10 The solution is q < 24. Since the inequality symbol is <, draw an open dot at 24 with an arrow to the left. a The solution is a x 8 The solution is x5. 5 with an arrow to the left. esolutions Manual - Powered by Cognero Page 10
11 The solution is. Since the inequality symbol is >, draw an open dot at The solution is. esolutions Manual - Powered by Cognero Page 11
4B Solve Inequalities by Addition or Subtraction
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b = 7 The y-intercept is 7.
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